Fred is

To set up the correct system of equations representing the situation involving Fred's and Nathan's ages, we translate the given statements into mathematical expressions.

1. "Fred is 4 times as old as Nathan" translates to:
\[
f = 4n
\]
where \( f \) is Fred's age and \( n \) is Nathan's age.

2. "Fred is also 27 years older than Nathan" translates to:
\[
f = n + 27
\]

Putting these two equations together, we have:
\[
\begin{cases}
f = 4n \\
f = n + 27
\end{cases}
\]

Now, let's look at the choices available:

- **Choice :
\[
\begin{cases}
f = 4n \\
f = n + 27
\end{cases}
\]

- **Choice B**:
\[
\begin{cases}
4f = n \\
f = n + 27
\end{cases}
\]

- **Choice C**:
\[
\begin{cases}
4f = n \\
f = n + 27
\end{cases}
\]

- **Choice D**:
\[
\begin{cases}
f = 4n \\
f = n - 27
\end{cases}
\]

The correct choice that represents the situation is **Choice :
\[
\begin{cases}
f = 4n \\
f = n + 27
\end{cases}
\]